Under the background of rapid global economic transformation, the influence of economic policy uncertainty (EPU) has penetrated all fields of production and life. It is significant to study how it affects the regional carbon emission intensity for regional sustainable development. Based on the data from 30 provinces from 2004 to 2017, this paper takes a complete account of spatial heterogeneity and the dynamic impact of economic policy uncertainty on carbon emission intensity using a spatial econometric model. The main conclusions are as follows: (1) For more than ten years, there have been significant differences and instabilities in economic policy uncertainty and carbon emission intensity in different regions of China. (2) China’s local carbon emission intensity shows an objective spatial aggregation effect, which is significant, spatially auto-correlated and clustered. (3) Based on the national level, economic policy uncertainty will significantly increase the regional carbon emission intensity. Additionally, economic policy uncertainty has a significant positive spatial spillover effect, which may increase carbon emission intensity in neighboring provinces. (4) Based on the provincial level, the impact of economic policy uncertainty on carbon emission intensity in various regions is significantly positive, with the most significant impact on the western region. Based on the above conclusions, the paper proposes policy suggestions to stabilize the regional carbon emission intensity in all directions.